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The 39th Root of 92

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Re: The 39th Root of 92

#61

Post by int_19h »

Turing_Machine wrote: post #46
pacaro wrote: post #17

Earlier quoted context omitted.

The thing that always gets me about this is how incomplete it is (at least in most people's experience) What is the unit of mass smaller than an Ounce? Some people know that this is a Grain (7,000 in a pound, which means the awfully convenient division of 437.5 per oz - assuming avoirdupois of course) What if anything is smaller than an inch? Power of two fractions until 1/64 then "thous" - 15.625 thous in 1/64" - al…

Most people never use units smaller than can be accounted for by fractional inches and ounces in their daily lives, and never did. The only people who ever used grains were pharmacists, jewelers, and the like. The only people who ever had to resort to thous were precision machinists and the like.

Open Amazon, and search for something as mundane as plastic bags or trash cans. Notice that their thickness is specified in "mils". How many people make purchasing decisions on those products, for use in their daily lives?

Re: The 39th Root of 92

#62

Post by disc »

HCIdivision17 wrote: post #20
kevhito wrote: post #18

Earlier quoted context omitted.

If you have never wired a house for electrical, then sure, the units seem arbitrary. But if you do, then the units seem very comfortable. 12ga for most typical 20a circuits, 14ga for light, 10ga or thicker for some heavy-duty circuits. Hey boss, we seem to be all out of 3.31mm^2 romex, all I got left is 2.08mm^2. And why did you mention cross-sectional area? Why not radius? or diameter? Or better yet, circumference?…

That's the trick. In a sense, the units follow the application, and hence English units always feel a bit natural. They have a tendency to have integer multiples and simple fractions. And when I say natural, I don't mean elegant. They often tend to be thoroughly arbitrary. But they match the needs, which is usually reasonably pragmatic. For example, 360 degrees is ideal for simple in-head directional geometry, but ra…

Wouldn't a much more natural unit for angular measurements be 1/(2*pi)? That way angular measurements are represented as their fraction of a circle (which is pretty easy to visualize; 180 degrees becomes 1/2.)

Re: The 39th Root of 92

#63

Post by dancek »

int_19h wrote: post #60
kevhito wrote: post #18

Earlier quoted context omitted.

If you have never wired a house for electrical, then sure, the units seem arbitrary. But if you do, then the units seem very comfortable. 12ga for most typical 20a circuits, 14ga for light, 10ga or thicker for some heavy-duty circuits. Hey boss, we seem to be all out of 3.31mm^2 romex, all I got left is 2.08mm^2. And why did you mention cross-sectional area? Why not radius? or diameter? Or better yet, circumference?…

The "it's more natural" argument, fielded by both sides, is largely a myth - take it from someone who lived in several countries and struggled with different units. Pretty much the only reason why something feels natural to you is because that's what you are accustomed to using. There's nothing more natural about an inch than a centimeter, and nice, round, easy-to-remember numbers can be had on both scales for "natur…

I don't know what's natural, but I live in Finland where we use the metric / SI system extensively. Some people don't even know how long an inch is, let alone a foot.

Recently I was building a roof with an old, very experienced builder. Turns out that on construction sites, nails and planks are always discussed in inches, even when they're actually metric. So a 60mm nail would be "a two point fiver" ("kakspuokki" or such in Finnish).

Re: The 39th Root of 92

#64

Post by jacobolus »

rm445 wrote: post #51
einhverfr wrote: post #28

Earlier quoted context omitted.

I am not sure. American units usually focus on divisibility and factoring of integers, while metric units focus on quick base-10 math. So they are different concerns and this is why, I think, people from elsewhere in the world have so much trouble understanding American units. If you are brought up with metric units, the units are built around the number system. A good way to understand the problem by for the HN audi…

Shout out to another base-12 fan. If only we had 12 fingers it might have happened. Arbitrary divisions of angle aren't very interesting, since the radian is so fundamental. But there is an angle system using multiples of 100: gradians. 100 is a quarter-turn and the internal angles of a triangle add up to 200. A lot of electronic calculators still offer them (the DRG button = degrees, radians, gradians).

Gradians are absolutely terrible. For everyday use, radians are also pretty impractical. I personally like just writing fractions of a full turn, but degrees/minutes/seconds aren’t too bad.

There are two cases where linear divisions of arclength-measured angles make sense: (1) the angles to make regular polygons of low numbers of sides, (2) repeated binary divisions, whose cartesian coordinates can be computed easily because we can just add two vectors and renormalize using an inverse square root which we know how to efficiently compute, and which are then nice for fixed point representations using binary integers in computers. For the first case, I think rational fractions of a turn work best; for the second case, I like binary angles (“brads”) https://en.wikipedia.org/wiki/Binary_scaling#Binary_angles ; losing the ability to precisely represent a thirds of a full turn is just one of those trade offs you sometimes need to make.

Otherwise, treating angle as a linear quantity with precise measurements (instead of some kind of approximations) is for most problems less useful than just using a cartesian coordinate representation for an angle (possibly keeping track of the coordinates squared if we want to stick to rational arithmetic.)

Radians are only really useful for solving calculus problems by hand, or writing academic math/science papers where it’s important to stick to established conventions. For practical computation radians are almost always an inferior choice, more computationally expensive and less precise (they’re built into lots of existing libraries, so can often be convenient despite the inefficiency).

Re: The 39th Root of 92

#65

Post by oxymoron »

kevhito wrote: post #18
ysleepy wrote: post #3

I continue to be baffled by the arcane units in the US. This uses a measure on the completely wrong abstraction level. An accidental production process now defines a wire unit instead the end result the consumer/engineer/technician wants to know (mm^2 or inch^2 oh no no it's pica^2 ?). There must be some sociological phenomenon going on that keeps the US from adopting modern units. Maybe can't admit a shortcoming and…

If you have never wired a house for electrical, then sure, the units seem arbitrary. But if you do, then the units seem very comfortable. 12ga for most typical 20a circuits, 14ga for light, 10ga or thicker for some heavy-duty circuits. Hey boss, we seem to be all out of 3.31mm^2 romex, all I got left is 2.08mm^2. And why did you mention cross-sectional area? Why not radius? or diameter? Or better yet, circumference?…

In Sweden, when running wiring we'll refer to the dimensions by monikers like "one and half squared", "six squared" and so on, corresponding to "1.5mm^2" etc. It has never felt very bulky to me, and doesn't seem like more effort than saying 14-gauge (or at least close enough).

If you're going to knock the other way, wouldn't t be far to at least check what that it is rather than making something up as a strawman?

Re: The 39th Root of 92

#66

Post by jolhoeft »

ysleepy wrote: post #15
MikeTLive wrote: post #8

Earlier quoted context omitted.

Appelbaum: So the people blocking adoption of the metric system weren't backward-looking traditionalists, but cutting-edge industrialists? Mihm: That's correct. While the anti-metric forces included outright cranks, including people who believed that the inch was a God-given unit of measurement, the most sophisticated and powerful opponents of the metric system were anything but cranks. They were engineers who built…

Yeah the engineers love the process of calculating if that wire can carry the specified current. Because it's so industry friendly. This is complete nonsense and sounds like musings of a desperate advocate. If you want to believe something, you start to accept the lamest arguments.

I actually did this a lot when I was designing electric motors. One detail the original article didn't note, is the 39th root of 92 is very close to the 6th root of 2, off by half a percent. This makes scaling for voltage changes simple. Going from US 120V to European 240V? Go up three wire gauges and double the number of turn.

In practice, it was not quite that simple, because of the half percent error, and wire insulation doesn't follow the same scaling pattern, but it was still quite handy, and much less trouble than metric, where you constantly had to dig out the wire gauge chart.

Re: The 39th Root of 92

#67

Post by jacobolus »

e2e8 wrote: post #59
jacobolus wrote: post #47

Earlier quoted context omitted.

If you have an industrial production process which is going to produce a set number of wire sizes, and you want them to be maximally useful for a wide variety of applications, you want a logarithmic scale. Responding to commenter e2e8: Using 2mm, 3mm, etc. would be substantially less functional. Once you have a log scale, it hardly matters whether you measure diameter or area, that’s just a constant factor. In the id…

You can plot out the wire gauges you want on a log scale and then round them to nice whole (metric measurement) numbers. That is in fact what is done for things like fasteners.

And then when you try to scale your whole design up, whoops, all the rounding changes and you need to redo everything.

Anyway, neither way here is right or wrong. One optimizes for uniformity of scaling, the other optimizes for intelligibility with a base ten number system.

Re: The 39th Root of 92

#68

Post by jacobolus »

einhverfr wrote: post #30
rz2k wrote: post #11

Earlier quoted context omitted.

The philosophy seems to be reversed with the ISO 216 paper size standards like A4. Anyway, the main advantage of metric seems to be its universality between different markets, rather than the somewhat silly idea of ideal relationships such as water in one arbitrary form having a certain weight and volume replacing a system that was derived from a hundreds of years process resembling a genetic algorithm.

I wonder if it is an internal/external optimization. The whole point of metric is that it is built around the number system, leading to easy conversion between units. The whole point of the American unit system is that they are optimized for specific use, but definitely not for conversion. ISO paper sizes are a great counterexample, actually, because they took an application, rather than a conversion-centric approach…

ISO paper sizes assume that content is scale-invariant.

US paper sizes assume that you have specific design sizes to your printing technology (picas) and then give you a grid of an even number of those units.

Graphic designers / typographers I know tend to prefer the US paper sizes.

Regular people who want to make photocopies of enlarged/reduced pages tend to prefer ISO sizes.

Re: The 39th Root of 92

#69

Post by function_seven »

HCIdivision17 wrote: post #20
kevhito wrote: post #18

Earlier quoted context omitted.

If you have never wired a house for electrical, then sure, the units seem arbitrary. But if you do, then the units seem very comfortable. 12ga for most typical 20a circuits, 14ga for light, 10ga or thicker for some heavy-duty circuits. Hey boss, we seem to be all out of 3.31mm^2 romex, all I got left is 2.08mm^2. And why did you mention cross-sectional area? Why not radius? or diameter? Or better yet, circumference?…

That's the trick. In a sense, the units follow the application, and hence English units always feel a bit natural. They have a tendency to have integer multiples and simple fractions. And when I say natural, I don't mean elegant. They often tend to be thoroughly arbitrary. But they match the needs, which is usually reasonably pragmatic. For example, 360 degrees is ideal for simple in-head directional geometry, but ra…

Regarding your PS: The most baffling measurements to me are tires. The diameter is expressed in inches, the width in millimeters, and the sidewall thickness is given as a percentage of tread width. So you get 255/40R17 to describe a 17” tire that's 10” wide with 4” sidewalls. (Or a 430mm tire that's 255mm wide with 100mm sidewalls)

Re: The 39th Root of 92

#70

Post by Hondor »

kevhito wrote: post #18
ysleepy wrote: post #3

I continue to be baffled by the arcane units in the US. This uses a measure on the completely wrong abstraction level. An accidental production process now defines a wire unit instead the end result the consumer/engineer/technician wants to know (mm^2 or inch^2 oh no no it's pica^2 ?). There must be some sociological phenomenon going on that keeps the US from adopting modern units. Maybe can't admit a shortcoming and…

If you have never wired a house for electrical, then sure, the units seem arbitrary. But if you do, then the units seem very comfortable. 12ga for most typical 20a circuits, 14ga for light, 10ga or thicker for some heavy-duty circuits. Hey boss, we seem to be all out of 3.31mm^2 romex, all I got left is 2.08mm^2. And why did you mention cross-sectional area? Why not radius? or diameter? Or better yet, circumference?…

Your example of mm is not true at all. There's no need for 3 significant figures for electrical wire size. Where I am, it's 2.5mm^2 for 10 A circuits, 1.0mm^2 for lighting, etc. The 2nd digit is always a 0 or a 5 so it's even simpler than it looks.
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